====== Sprinkler Experiment ======

<div center round 50% alert>
FIXME Work in progress.  Translating from old Wiki markup.
</div>

===== Summary =====

Evidence suggests that the two recent sprinkler pipe breaks occurred because the wet pipe got too cold.  Some possible remedies have been suggested.  To determine whether they may be effective some of these remedies were simulated in the small office and temperature readings were collected.  These temperatures were compared to outdoor temperatures to evaluate their effects.  It was found that inserting a vent in the valence would have provided warming benefits sufficient to prevent the past breaks.  Also insulating the drywall from the outside and moving the wet pipe inside the vapour barrier improved warming further.

===== Introduction =====

Around 2006-11-28 and again on 2008-12-20 sprinkler pipes spontaneously burst, flooding several homes.  Many possible issues have been presented to the strata council to try and explain these two pipe failures.  Even more solutions have been proposed.  In short, the breaks are believed to be due to extremely cold weather and all of the solutions aim to warm the pipe where the breaks have occurred.  Some of the solutions have been severe (eg. installing an 18-by-18 inch box in the ceiling in front of the valence in every living room).  

Such severe solutions may solve the heat problem but introduce others: for example, the aesthetics of living rooms could be diminished which may impact property values.  Instead, it would be prudent to test simpler, less invasive solutions first to see if they can sufficiently warm the wet pipe.

The valence in the small office has been opened up to allow engineers and contractors to see the situation.  This makes for an excellent testbed of these simple solutions.  The remedies can be mimicked fairly simply and temperatures at the wet pipe measured to see how much they contribute to warming of the pipe.

In the next section we describe the experimental setup and the treatments that were applied.  Data analysis follows, where raw temperature data are converted to a measure of effectiveness.  Results show that each intervention provides extra warming and together they work synergistically to contribute more benefit.  We conclude that applying these interventions will be sufficient to protect the pipes from breaks due to cold weather in the future.

===== Methods =====

A hole roughly 8 inches tall by 16 inches wide has been cut into the wall of the valence in the small office.  The hole was cut to give access to investigators to inspect the sprinkler pipe assembly for themselves.  This hole presents an opportunity to try several interventions to test their ability to provide warmth to the wet pipe.

The pipe temperature can be measured via Rik's electronic outdoor thermometer.  The thermometer is available for inspection.  It consists of a small probe on the end of a thin, long (approx 10 foot) wire.  A digital display shows the temperature in Celsius to 0.1C precision.  It has been used for years to monitor outdoor temperatures and is expected to be accurate within 1C.

The temperature probe was placed next to the wet pipe (within 2 inches of the junction of where the pipe breaks occurred).  The valence was then altered to try and approximate the different conditions under investigation.

==== Concepts ====

=== Temperature Profile ===


When the temperature outside is colder than inside then heat flows from inside, through the wall, to outside.  The temperature along this heat gradient is higher near the inside wall and lower near the outside.  Consider a cross section of the wall with the warm interior on one side and the cold exterior on the other.  One can imagine a "temperature profile" where the temperature falls as one proceeds through the cross section from inside to outside.  The temperature profile will probably not be linear, it will depend on the thermal properties of the materials in the wall.  The temperature will fall slowly as we move through the cross section where there is good insulation and quickly where there is poor insulation.  See [(:ref:Lstiburek04)] for a fuller explanation of a wall's temperature profile.

<div round box right>
(:graph width=500; height=300; xmax=9.5; xmin=-2.5; ymax=24; ymin=-0.2*ymax; axes(1,5,"labels",1,1);    stroke="black"; path([[0,22],[2,13],[6,10],[8,2]]);     fontsize=16; text([0.8*xmax/2,ymin],"cross section (inches)", above); text([-0.5,0.97*ymax],"temperature", belowleft); text([-0.5,0.92*ymax],"profile (C)", belowleft);    text([0,12.5],"inside",left); text([8,12.5],"outside",right); strokewidth=5;    stroke="red"; line([0,0],[0,ymax]);    stroke="blue"; line([8,0],[8,ymax]); :)

[[#Figure1]]Figure 1: Example temperature profile through the cross section of a wall.  Inside is warm, outside is cold, and the temperature drops continuously (but not necessarily smoothly) from inside to out.
</div>

=== Fractional Insulation ===

The temperatures throughout the cross section will vary hourly as indoor and outdoor temperatures change.  But the thermal properties of the wall depend only on its materials and construction.  If we pick a location somewhere in the cross section we will find that its temperature is closer to the inside or outside temperature, depending on the thermal properties of the wall.  For example, in [[#Figure1|Figure 1]] the temperature at 2 inches is 13C, or 65% of the way towards the inside temperature of 22C (versus 2C outside).  While the temperatures may vary, we expect the thermal properties of the wall to remain constant so, in our example, the temperature at 2 inches should always be 65% towards the inside temperature (regardless of what the inside and outside temperatures are).

Let us define the "fractional insulation", \(fI\), that describes the thermal properties at a given point in the cross section.  Given a temperature \(T\) at the point, \(T_\text{in}\) inside, and \(T_\text{out}\) outside, the fractional insulation is

\[
  fI = \frac{T - T_\mathrm{out}}{T_\mathrm{in} - T_\mathrm{out}}.
\]

The fractional insulation can then vary from 0 to 100%, which represents how well insulated the given point is, compared to the total insulation provided by the wall.  If \(fI=0\%\) then the point is uninsulated, effectively outside.  In the other extreme, \(fI=100\%\), the point is always as warm as the room, it is fully insulated.  Points in the cross section of the wall will be found in the range \(0\% < fI < 100\% \), where higher values indicate more heating from the room.  Fractional insulation is equivalent to the ratio of the R-value up to a point in the wall versus the R-value of the entire wall.  Our goal will be to manipulate the thermal properties of the sprinkler pipe to increase its fractional insulation.

We should expect the temperature at the wet pipe in the wall to vary, depending on the inside and outside temperature.  So we can not rely on temperature itself as a measure of effectiveness of each intervention.  The fractional insulation, on the other hand, is a measure of the thermal properties in the wall itself, and as such shouldn't depend on changes in temperature.  So, by finding and using the fractional insulation we will be able to extrapolate our findings to hypothetical outdoor conditions.  For example, using this technique we will be able to predict the thermal tolerances of each intervention (how cold it can get outside before we expect the pipe to break).

==== Treatments ====

The opening in the wall in the small office provided an opportunity to try changing the thermal properties around the sprinkler pipe.  The thermometer could then be used to estimate the fractional insulation \(fI\) at the pipe under each treatment.  Four different treatments were considered in a 2x2 factorial design (meaning that each of two "factors" can take on two values):
(:table cellspacing="2" cellpadding="6" align="center" bgcolor="#ccc":)
(:cellnr:)
(:cell:)
(:cell bgcolor="white" colspan="2" align="center":)Insulation and vapour barrier
(:cellnr:)
(:cell:)
(:cell bgcolor="white" align="center":)No
(:cell bgcolor="white" align="center":)Yes
(:cellnr bgcolor="white" rowspan="2" valign="middle":)Heat register
(:cell bgcolor="white" align="center" valign="middle":)No
(:cell bgcolor="white" align="center" valign="middle":)[[#FactorControl|Control]]
(:cell bgcolor="white" align="center" valign="middle":)[[#FactorInsulation|Insulation and vapour barrier]]
(:cellnr bgcolor="white" align="center" valign="middle":)Yes
(:cell bgcolor="white" align="center" valign="middle":)[[#FactorRegister|Heat register]]
(:cell bgcolor="white" align="center" valign="middle":)[[#FactorBoth|Both insulation and register]]
(:tableend:)

=== Control [[#FactorControl]] ===

  * Insulation and vapour barrier = No
  * Heat register = No

The conditions of the valence since the rainscreening were approximated.  Plastic was taped down around the the wet pipe separating it from the valence interior to simulate the vapour barrier that trapped the wet pipe on the outside with the cold exterior air.  (The vapour barrier had previously been cut away for inspectors.)  Finally, the opening in the drywall was closed.  See [[#Figure2|Figure 2]], below, for a schematic representation.

=== Insulation and vapour barrier [[#FactorInsulation]] ===

  * Insulation and vapour barrier = Yes
  * Heat register = No

It was observed by engineers, contractors, and strata council that the sprinkler pipe that penetrates the exterior wall is not properly insulated so cold air can flow into the valence and cool the wet pipe.  It was also noted that the vapour barrier encapsulates the wet pipe on the exterior side of the wall, so it is in closer thermal contact with outside than inside.

This treatment simulates correction of both these conditions.  A rag was stuffed into the air gap surrounding the sprinkler pipe to reduce the flow of cold air from inside.  Then a layer of plastic was taped down on the outside of the wet pipe, simulating the movement of the vapour barrier.  See [[#Figure2|Figure 2]], below, for a schematic representation.

=== Heat register [[#FactorRegister]] ===

  * Insulation and vapour barrier = No
  * Heat register = Yes

Engineers recommended installing a heat register in the interior wall as a temporary fix.  It should provide more heat to the wet pipe, offsetting the heat it loses to outside.

This treatment simulates the effect of just installing a heat register.  The insulation was removed and the "vapour barrier" moved to the inside of the wet pipe (like the control treatment).  Then the opening in the drywall was partially covered with a rag to leave roughly the same size opening as a 4x10 inch heat register would provide.  See [[#Figure2|Figure 2]], below, for a schematic representation.

=== Both insulation and register [[#FactorBoth]] ===

  * Insulation and vapour barrier = Yes
  * Heat register = Yes

Finally, both the effects of adding insulation and a heat register were simulated.  A rag was stuffed around the pipe to provide insulation, the "vapour barrier" was taped down outside of the wet pipe, and the opening in the drywall was partially uncovered.

<div round box right>
(:table cellspacing="2" cellpadding="6" align="center" bgcolor="#ccc":)
(:cellnr:)
(:cell:)
(:cell bgcolor="white" colspan="2" align="center":)Insulation and vapour barrier
(:cellnr:)
(:cell:)
(:cell bgcolor="white" align="center":)No
(:cell bgcolor="white" align="center":)Yes
(:cellnr bgcolor="white" rowspan="2" valign="middle":)Heat register
(:cell bgcolor="white" align="center" valign="middle":)No
(:cell bgcolor="white" align="center":)%width=100pct% [[Attach:WallCrossSectionCurrent.png | Attach:WallCrossSectionCurrent.png]] [[<<]] [[#FactorControl|Control]]
(:cell bgcolor="white" align="center":)%width=100pct% [[Attach:WallCrossSectionInsulationAndVapourBarrier.png | Attach:WallCrossSectionInsulationAndVapourBarrier.png]] [[<<]] [[#FactorInsulation|Insulation and vapour barrier]]
(:cellnr bgcolor="white" align="center" valign="middle":)Yes
(:cell bgcolor="white" align="center":)%width=100pct% [[Attach:WallCrossSectionHeatRegister.png | Attach:WallCrossSectionHeatRegister.png]] [[<<]] [[#FactorRegister|Heat register]]
(:cell bgcolor="white" align="center":)%width=100pct% [[Attach:WallCrossSectionBoth.png | Attach:WallCrossSectionBoth.png]] [[<<]] [[#FactorBoth|Both insulation and register]]
(:tableend:)
[[#Figure2]]Figure 2: Schematic representation of the four experimental treatments.  In the unaltered, control condition (top left), cold air can readily get to the wet pipe but warm air from inside is blocked.  In the insulation and vapour barrier treatment (top right), both warm and cold air are blocked.  In the heat register treatment (bottom left), warm and cold air mix at the wet pipe.  When both interventions are applied (bottom right), cold air is blocked and warm air from inside reaches the wet pipe.  (Drawings are not to scale.)
</div>

==== Data acquisition ====

The goal was to compute the fractional insulation \(fI\) at the wet pipe for each treatment.  To do so it was necessary to acquire temperature data at the pipe for each treatment and compare it against the inside and outside temperatures for the same period.  

=== Pipe temperature ===

The pipe temperature was measured using a digital outdoor thermometer with a small temperature probe at the end of a thin, 10-foot line. The probe was taped to the wet pipe and left in place for all treatments.  Because it was on a long line temperature readings could be taken without disturbing the experiments.  The protocol for each treatment was as follows:
# Setup: Alter the wall by installing/removing the "insulation", "vapour barrier", and/or "heat register" as dictated by each treatment.
# Transient: Wait until the temperature stabilizes.  The act of altering the wall briefly let a lot of warm air in so the temperature at the pipe was not immediately indicative of the treatment conditions.  The pipe needed time to reach a new stable temperature.  The temperature was measured, typically every three hours until it stabilized.  Stabilization was defined as the first reversal of the trend.  (For example, if the temperature was dropping steadily after setup then it was assumed to have stabilized when it increased.)  The temperature typically stabilized 4-6 hours after setup.  The temperatures for this transient period were excluded from analysis.
# Data collection: After the temperature stabilized it was recorded, roughly every three hours, for a period of 24 hours.  These temperatures were used to calculate the fractional insulation \(fI\) for the given treatment.

=== Indoor temperature ===

Before the very beginning of the experiment the thermostat in the room was set for 22C and then left there throughout all treatments, to approximate living conditions in a home.  Only one temperature probe was available so the indoor temperatures could not be accurately measured simultaneous to the pipe temperatures.  Instead, a final experiment was performed where the temperature probe was left in the room, far from the outside wall and the heater, near the thermostat.  Again, temperatures were recorded over a 24 hour period.  The outdoor conditions over the period of the entire experiment were luckily very stable so it is reasonable to expect that the recorded indoor temperatures were good representations of the indoor temperatures during each treatment period (because there wouldn't have been much change in cooling rates).

=== Outdoor temperature ===

The outdoor temperatures were not measured directly. Instead, hourly data was collected from [[http://www.climate.weatheroffice.gc.ca/climateData/hourlydata_e.html?timeframe=1&Prov=XX&StationID=889&Year=2009&Month=12&Day=1|Environment Canada]] and the outdoor temperatures for the same time as the pipe readings were recorded.  Although the temperature reported is from the airport rather than directly outside the wall, this method is more useful because more data are available.  For example, we don't have temperature data for directly outside the wall when the pipes broke in 2006 & 2008--but Environment Canada does.  For our purposes, it is not necessary to have the exact outside temperature.  The method of calculating the fractional insulation is robust to systematic errors (because we can consider the wall to be in thermal contact--albeit over a long distance--with the airport).  But we acknowledge that using airport temperatures introduces statistical errors--we assume they are small.

===== Data =====

==== Experiment 0: Indoor temperature ====

To find the fractional insulation \(fI\) for each treatment it is first necessary to establish the indoor temperature \(T_\text{in}\).  By measuring temperatures over 24 hours we find an average

\[
  T_\mathrm{in} = 22.1C
\]

It is also useful to establish the confidence limits of the indoor temperature.  The data indicates the indoor temperature lies in the range 17.9C to 26.4C (within 2 standard deviations) 95% of the time. We will use this information later to compute confidence limits for the effectiveness of each treatment.
 
{{url>http://www.editgrid.com/publish/html/user/rikblok/66217436/?bgcolor=%23ffffff&fgcolor=%23000000&version=2&frame_style=border%3A9px%20solid%20%23666%3Bheight%3A100%25%3Bwidth%3A100%25&password=RBo53d3%24 500}}

Having the indoor and outdoor temperatures it remains only to measure the temperature at the wet pipe for each treatment. From that we can compute the fractional insulation.

==== Experiment 1: Control treatment ====

<div round box right>
(:table cellspacing="2" cellpadding="6" align="center" bgcolor="#ccc":)
(:cellnr bgcolor="white" align="center":)%width=100pct% [[Attach:SprinklerExperimentOriginalVapourBarrier.JPG | Attach:SprinklerExperimentOriginalVapourBarrier.JPG]] [[<<]]
(a) Original position of vapour barrier
(:cell bgcolor="white" align="center":)%width=100pct% [[Attach:SprinklerExperimentClosedValence.JPG | Attach:SprinklerExperimentClosedValence.JPG]] [[<<]] (b) Closed valence
(:tableend:)
[[#Figure3]]Figure 3: Alterations made to valence to replicate control conditions for Experiment 1.  Plastic covers the wet pipe (a) to replicate the original position of the vapour barrier and the valence is closed (b).
</div>

{{url>http://www.editgrid.com/publish/html/user/rikblok/66217437/?bgcolor=%23ffffff&fgcolor=%23000000&version=2&frame_style=border%3A9px%20solid%20%23666%3Bheight%3A100%25%3Bwidth%3A100%25&password=RBo53d3%24 500}}

==== Experiment 2: Insulation treatment ====

<div round box right>
(:table cellspacing="2" cellpadding="6" align="center" bgcolor="#ccc":)
(:cellnr bgcolor="white" align="center":)%width=100pct% [[Attach:SprinklerExperimentInsulationAndVapourBarrier.JPG | Attach:SprinklerExperimentInsulationAndVapourBarrier.JPG]] [[<<]]
(a) Rag (red) forced in gap around sprinkler pipe and plastic moved to outside of wet pipe
(:cell bgcolor="white" align="center":)%width=100pct% [[Attach:SprinklerExperimentClosedValence.JPG | Attach:SprinklerExperimentClosedValence.JPG]] [[<<]] (b) Closed valence
(:tableend:)
[[#Figure4]]Figure 4: Alterations made to valence to replicate insulation treatment for Experiment 2.  A rag simulates the effect of insulating the gap where the pipe penetrates the exterior wall and plastic creates a vapour barrier between the outside and the wet pipe (a).  The valence is closed (b).
</div>

{{url>http://www.editgrid.com/publish/html/user/rikblok/66217438/?bgcolor=%23ffffff&fgcolor=%23000000&version=2&frame_style=border%3A9px%20solid%20%23666%3Bheight%3A100%25%3Bwidth%3A100%25&password=RBo53d3%24 500}}

==== Experiment 3: Register treatment ====

<div round box right>
(:table cellspacing="2" cellpadding="6" align="center" bgcolor="#ccc":)
(:cellnr bgcolor="white" align="center":)%width=100pct% [[Attach:SprinklerExperimentOriginalVapourBarrier.JPG | Attach:SprinklerExperimentOriginalVapourBarrier.JPG]] [[<<]]
(a) Original position of vapour barrier
(:cell bgcolor="white" align="center":)%width=100pct% [[Attach:SprinklerExperimentVent.JPG | Attach:SprinklerExperimentVent.JPG]] [[<<]] (b) Drywall is left partially open to simulate a heat register
(:tableend:)
[[#Figure5]]Figure 5: Alterations made to valence to replicate heat register treatment for Experiment 3.  Plastic covers the wet pipe (a) to replicate the original position of the vapour barrier.  The valence is partially open to simulate the effect of having a heat register in the wall, allowing warm air from the room in (b).
</div>

{{url>http://www.editgrid.com/publish/html/user/rikblok/66389565/?bgcolor=%23ffffff&fgcolor=%23000000&version=2&frame_style=border%3A9px%20solid%20%23666%3Bheight%3A100%25%3Bwidth%3A100%25&password=RBo53d3%24 500}}

==== Experiment 4: Both ====

<div round box right>
(:table cellspacing="2" cellpadding="6" align="center" bgcolor="#ccc":)
(:cellnr bgcolor="white" align="center":)%width=100pct% [[Attach:SprinklerExperimentInsulationAndVapourBarrier.JPG | Attach:SprinklerExperimentInsulationAndVapourBarrier.JPG]] [[<<]]
(a) Rag (red) forced in gap around sprinkler pipe and plastic moved to outside of wet pipe
(:cell bgcolor="white" align="center":)%width=100pct% [[Attach:SprinklerExperimentVent.JPG | Attach:SprinklerExperimentVent.JPG]] [[<<]] (b) Drywall is left partially open to simulate a heat register
(:tableend:)
[[#Figure6]]Figure 6: Alterations made to valence to replicate insulation treatment for Experiment 4.  A rag simulates the effect of insulating the gap where the pipe penetrates the exterior wall and plastic creates a vapour barrier between the outside and the wet pipe (a).  The valence is partially open to simulate the effect of having a heat register in the wall, allowing warm air from the room in (b).
</div>

{{url>http://www.editgrid.com/publish/html/user/rikblok/66389964/?bgcolor=%23ffffff&fgcolor=%23000000&version=2&frame_style=border%3A9px%20solid%20%23666%3Bheight%3A100%25%3Bwidth%3A100%25&password=RBo53d3%24 500}}

===== Results =====

==== Fractional insulation ====

The above experiments allow to calculate the fractional insulation provided by each treatment.  Recall, the fractional insulation represents the amount of insulation at the wet pipe compared to the insulation of the entire wall.  The results are shown in the data table and chart below.

{{url>http://www.editgrid.com/publish/html/user/rikblok/66456133/?bgcolor=%23ffffff&fgcolor=%23000000&version=2&frame_style=border%3A9px%20solid%20%23666%3Bheight%3A100%25%3Bwidth%3A100%25&password=RBo53d3%24 500}}

We find that the application of a heat register //significantly// increases (with more than 95% confidence) the fractional insulation compared to the control (which represents current conditions).  Applying both the register and insulation provides further warming benefits.

==== Pipe break temperature ====

We now know the fractional insulation at the wet pipe under the current (control) conditions.  We can also look up the actual outside temperature when the pipe broke in 2006 & 2008.  Using this information we can reverse the formula for the fractional insulation in order to estimate the the wet pipe temperature when the break occurred.  The results may not be exact because we have to guess how warm it was inside each home at the time of the break but it will give us an important result: whether the temperature at the wet pipe was near or below freezing when it broke.  If the pipe froze then the break would have been due to the expansion of ice forming in the pipe.  On the other hand, if the wet pipe was still above freezing temperature then we can surmise that it was due to uneven contraction at the plastic/iron juncture.  We will also use the pipe break temperature to forecast the outdoor temperature each treatment will permit to estimate the risk of future breaks.

From the fractional insulation formula, the wet pipe temperature, \(T\), would be 

\[
  T = T_\text{out} + fI (T_\text{in} - T_\text{out}).
\]

{{url>http://www.editgrid.com/publish/html/user/rikblok/66458379/?bgcolor=%23ffffff&fgcolor=%23000000&version=2&frame_style=border%3A9px%20solid%20%23666%3Bheight%3A100%25%3Bwidth%3A100%25&password=RBo53d3%24 500}}

The data indicate that the mean outdoor temperatures on the days of the breaks were -8.2C (2006-11-28) and -10.3C (2008-12-20), the two coldest days on record since 1999.  Conversely, no pipes broke on the next coldest day (-7.8C on 2004-01-04).  Applying the above formula we can estimate the temperature at the pipe on these days: it appears the wet pipe did not break at +7.4C (2004) but did break at +7.2C (2006).  This suggests the threshold break temperature at the wet pipe is 

\[
  T_\text{pipe}^\text{break} = 7.3C.
\]

We find the chance that the pipe was at or below freezing when it burst is negligible.

==== Outdoor break temperature ====

We can use our knowledge of the wet pipe threshold temperature to estimate the tolerances of each treatment: how cold it could get outside with each temperature before the pipe is in danger of breaking.  We do this by reorganizing our equation:

\[
  T_\text{out}^\text{break} = \frac{T_\text{pipe}^\text{break} - fI \, T_\text{in}}{1 - fI}
\]

where \(T_\text{pipe}^\text{break}=7.3C\) is the critical break temperature at the pipe.  From this we can compute \(T_\text{out}^\text{break}\), the outside temperature that would result in the wet pipe reaching the break threshold under each treatment.

{{url>http://www.editgrid.com/publish/html/user/rikblok/66655697/?bgcolor=%23ffffff&fgcolor=%23000000&version=2&frame_style=border%3A9px%20solid%20%23666%3Bheight%3A100%25%3Bwidth%3A100%25&password=RBo53d3%24 500}}

As shown in the above table and chart, each treatment is expected to improve the wet pipe's resilience to outdoor cold, compared to the current (control) condition.  In particular, the register treatment is //significantly// better than the current condition.  We should then also expect that applying //both// the register and insulation should be better than the control (but the larger error margins reduces our confidence).  

For comparison, the record cold temperature in Vancouver since 1937, -17.8C, is also shown.  We find that both treatments that involve insertion of a heat register are expected to protect to temperatures exceeding this record cold.  Note that the error margins don't permit certainty, but this is suggestive that either treatment should be adequate for our needs.

===== Conclusions =====

Since 2006 the building has experienced two sprinkler pipe breaks attributed to cold weather.  It is necessary to increase the warmth of the wet pipe.  By manipulating an open wall it was possible to simulate the conditions of some proposed remedies and determine their effectiveness.  

Two modifications were considered in a 2-by-2 factorial experiment: (1) improving the insulation of the wet pipe from outside and (2) inserting a heat register in the inside wall.  

It was found that improving the insulation (and modifying the vapour barrier) may provide warmth on its own but the results were not significant.  However, inserting a heat register did provide a significant heating benefit and should prevent future breaks.  Applying both modifications was found to further warm the pipe.

It was also discovered in the course of the experiment that the wet pipe most likely did not break due to freezing.  Instead, we hypothesize it was due to uneven contraction during cooling across the material junction where the iron joins the polymer (PVC?) pipe.

In conclusion, the experiment shows that adding a heat register should provide sufficient warmth to the wet pipe to prevent future breaks.  Insulating the pipe from outside and moving the vapour barrier is less effective but also contributes to warming the pipe.

===== References =====

~~REFNOTES cite~~